Sahin M.Tan E.Yilmaz S.2020-06-252020-06-25201914505444https://doi.org/10.30755/NSJOM.07284https://hdl.handle.net/20.500.12587/2663In this paper, we present a further generalization of the bi-periodic Fibonacci quaternions and octonions. We give the generating function, the Binet formula, and some basic properties of these quaternions and octonions. The results of this paper not only give a generalization of the bi-periodic Fibonacci quaternions and octonions, but also include new results such as the matrix representation and the norm value of the generalized bi-periodic Fibonacci sequence. © 2019 Novi Sad Journal of Mathematics. All rights reserved.eninfo:eu-repo/semantics/closedAccessBi-periodic Fibonacci sequenceFibonacci sequenceOctonionsQuaternionsArticle491677910.30755/NSJOM.072842-s2.0-85070684217Q4